Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If a triangle has sides of lengths 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

Can a triangle have side lengths of 0, 11, and 12?

Back

No, because one side length is 0, which does not satisfy the Triangle Inequality Theorem.

Front

Which of the following sets of lengths can form a triangle: (5, 7, 12) or (5, 7, 11)?

Back

(5, 7, 11) can form a triangle because 5 + 7 > 11. (5, 7, 12) cannot form a triangle because 5 + 7 < 12.

Front

What must be true about the longest side of a triangle?

Back

The longest side must be less than the sum of the other two sides.

Front

If the longest side of a triangle is 10, what must be true about the other two sides?

Back

The sum of the other two sides must be greater than 10.

Front

Determine if a triangle can be formed with sides of lengths 15 in., 12 in., and 2 in.

Back

No, because 15 + 12 is not greater than 2.

Front

Which lengths cannot represent the sides of a triangle: 28, 30, 58 or 32, 34, 60?

Back

28, 30, 58 cannot represent the sides of a triangle.

Front

What is an example of side lengths that can form a triangle?

Back

Side lengths of 7, 8, and 9 can form a triangle.

Front

If two sides of a triangle are 6 and 8, what is the range of possible lengths for the third side?

Back

The third side must be greater than 2 and less than 14.